Top 10 Most Famous Thought Experiments

Thought experiments are mental concepts or hypotheses, often resembling riddles, which are used by philosophers and scientists as simple ways of illuminating what are usually very dense ideas. Most often, they’re used in more abstract fields like philosophy and theoretical physics, where physical experiments aren’t possible. They serve as some hearty food for thought, but given their complex subject matter, it’s not unusual for even the thought experiment itself to be nearly incomprehensible. With this in mind, here are ten of the most famous thought experiments, along with explanations of the philosophical, scientific, and ethical ideas they work to explain:

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10. The Trolley Problem

One of the most well known thought experiments in the field of ethics is the “Trolley Problem,” which goes something like this: a madman has tied five innocent people to a trolley track. An out of control trolley car is careening toward them, and is moments away from running them over. Luckily, you can pull a lever and divert the trolley to another track. The only problem is that the madman has also tied a single person to that track. Considering the circumstances, should you pull the lever?

What it Means:

The trolley problem was first proposed by the philosopher Philippa Foot as a means of critiquing the major theories in ethical philosophy, in particular utilitarianism, the system which proposes that the most moral decision is always the one that provides “the greatest good for the greatest number.” From a utilitarian point of view, the obvious choice is to pull the lever, saving five and only killing one. But critics of this theory would state that in pulling the lever you become complicit in what is clearly an immoral act—you are now partially responsible for the death of the lone person on the other track. Others, meanwhile, argue that your mere presence in the situation demands that you act, and that to do nothing would be equally immoral. In short, there is no wholly moral action, and this is the point. Many philosophers have used the trolley problem as an example of the ways that real world situations often force individuals to compromise their own moral codes, and that there are times when there is no totally moral course of action.

9. The Cow in the Field

One of the major thought experiments in epistemology (the field of philosophy that deals with knowledge) is what is known as “The Cow in the Field.” It concerns a farmer who is worried his prize cow has wandered off. When the milkman comes to the farm, he tells the farmer not to worry, because he’s seen that the cow is in a nearby field. Though he’s nearly sure the man is right, the farmer takes a look for himself, sees the familiar black and white shape of his cow, and is satisfied that he knows the cow is there. Later on, the milkman drops by the field to double-check. The cow is indeed there, but it’s hidden in a grove of trees. There is also a large sheet of black and white paper caught in a tree, and it is obvious that the farmer mistook it for his cow. The question, then: even though the cow was in the field, was the farmer correct when he said he knew it was there?

What it Means:

The Cow in the Field was first used by Edmund Gettier as a criticism of the popular definition of knowledge as “justified true belief”—that is, that something becomes knowledge when a person believes it; it is factually true; and they have a verifiable justification for their belief. In the experiment, the farmer’s belief that the cow was there was justified by the testimony of the milkman and his own verification of a black and white object sitting in the field. It also happened to be true, as the milkman later confirmed. But despite all this, the farmer did not truly know the cow was there, because his reasoning for believing it turned out to be based on false premises. Gettier used this experiment, along with a few other examples, as proof of his argument that the definition of knowledge as justified true belief needed to be amended.

8. The Ticking Time Bomb

If you’ve paid any attention to political discourse over the past few years—or ever seen an action movie, for that matter—then you are no doubt familiar with the “ticking time bomb” thought experiment. It asks you to imagine that a bomb or other weapon of mass destruction is hidden in your city, and the timer on it will soon strike zero. You have in your custody a man with knowledge of where the device is planted. Do you resort to torture in order to get him to give up the information?

What it Means:

Like the trolley problem, the ticking time bomb scenario is an ethical problem that forces one to choose between two morally questionable acts. It is most often employed as a counter argument to those who say the use of torture is inexcusable under any circumstances. It’s also used as an example of the way laws—like those the U.S. has against torturing prisoners—will always be set aside given extreme circumstances. Thanks to its fictionalized use in television shows like 24, along with its constant position in political debates, the ticking time bomb scenario has become one of the most frequently repeated thought experiments. An even more extreme take on the problem was presented in a British news article earlier this year. That version proposes that the terrorist in question won’t respond to torture, and asks if one would be willing to resort to torturing the man’s wife and children as a means of extracting the information from him.

7. Einstein’s Light Beam

It’s a little known fact that Albert Einstein’s famous work on special relativity was spurred by a thought experiment he conducted when he was only 16 years old. In his book Autobiographical Notes, Einstein recalls how he once daydreamed about chasing a beam of light as it traveled through space. He reasoned that if he were able to move next to it at the speed of light, he should be able to observe the light frozen in space as “an electromagnetic field at rest though spatially oscillating.” For Einstein, this thought experiment proved that for his imaginary observer “everything would have to happen according to the same laws as for an observer who, relative to the Earth, was at rest.”

What it Means:

In truth, no one really knows for sure. Scientists have long debated how this deceivingly simple thought experiment helped Einstein make the massive theoretical leap required to arrive at special relativity theory. At the time, the ideas in the experiment contradicted the now-debunked belief in the “aether,” an invisible field through which light was believed to travel. It would be years before he could prove he was right, but this thought experiment was somehow the “germ,” as he called it, for Einstein’s theory of special relativity, one of the ideas that first established him as a towering figure in theoretical physics.

6. The Ship of Theseus

One of the oldest of all thought experiments is the paradox known as the Ship of Theseus, which originated in the writings of Plutarch. It describes a ship that remained seaworthy for hundreds of years thanks to constant repairs and replacement parts. As soon as one plank became old and rotted, it would be replaced, and so on until every working part of the ship was no longer original to it. The question is whether this end product is still the same Ship of Theseus, or something completely new and different. If it’s not, at what point did it stop being the same ship? The Philosopher Thomas Hobbes would later take the problem even further: if one were to take all the old parts removed from the Ship of Theseus and build a new ship from them, then which of the two vessels is the real Ship of Theseus?

What it Means:

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For philosophers, the story of the Ship of Theseus is used as a means of exploring the nature of identity, specifically the question of whether objects are more than just the sum of their parts. A more modern example would be a band that had evolved over the years to the point that few or no original members remained in the lineup. This notion is also applicable to everything from businesses, which might retain the same name despite mergers and changes in leadership, to the human body, which is constantly regenerating and rebuilding itself. At its heart, the experiment forces one to question the commonly held idea that identity is solely contained in physical objects and phenomena.

5. Galileo’s Gravity Experiment

One of the earliest thought experiments originated with the physicist and astronomer Galileo. In order to refute Aristotle’s claim that the speed of a falling object is dictated by its mass, Galileo devised a simple mental example: According to Aristotelian logic, if a light object and a heavy object were tied together and dropped off a tower, then the heavier object would fall faster, and the rope between the two would become taut. This would allow the lighter object to create drag and slow the heavy one down. But Galileo reasoned that once this occurs, the weight of the two objects together should be heavier than the weight of either one by itself, therefore making the system as a whole fall faster. That this is a contradiction proved that Aristotle’s hypothesis was wrong.

What it Means:

One of the most famous stories about Galileo is that he once dropped two metal balls off the Leaning Tower of Pisa to prove that heavier objects do not fall faster than lighter ones. In actuality, this story is probably just a legend; instead, it was this elegant thought experiment that helped prove a very important theory about gravity: no matter their mass, all objects fall at the same rate of speed.

4. Monkeys and Typewriters

Another thought experiment that gets a lot of play in popular culture is what is known as the “infinite monkey theorem.” Also known as the “monkeys and typewriters” experiment, the theorem states that if an infinite number of monkeys were allowed to randomly hit keys on an infinite number of typewriters for an infinite amount of time, then at some point they would “almost surely” produce the complete works of Shakespeare. The monkeys and typewriters idea was popularized in the early 20th century by the French mathematician Emile Borel, but its basic idea—that infinite agents and infinite time will randomly produce anything and everything—dates back to Aristotle.

What it Means:

Simply put, the “monkeys and typewriters” theorem is one of the best ways to illustrate the nature of infinity. The human mind has a difficult time imagining a universe with no end or time that will never cease, and the infinite monkeys help to illustrate the sheer breadth of possibilities these concepts create. The idea that a monkey could write Hamlet by accident seems counterintuitive, but in fact it is mathematically provable when one considers the probabilities. The theorem itself is impossible to recreate in the real world, but that hasn’t stopped some from trying: In 2003, science students at a zoo in the U.K. “tested” the infinite monkey theorem when they put a computer and a keyboard in a primate enclosure. Unfortunately, the monkeys never got around to composing any sonnets. According to researchers, all they managed to produce was five pages consisting almost entirely of the letter “s.”

3. The Chinese Room

The Chinese Room is a famous thought experiment first proposed in the early 1980s by John Searle, a prominent American philosopher. The experiment asks you to imagine that an English speaking man has been placed in a room that is entirely sealed, save for a small mail slot in the chamber door. He has with him a hard copy in English of a computer program that translates the Chinese language. He also has plenty of spare scratch paper, pencils, and file cabinets. Pieces of paper containing Chinese characters are then slipped through the slot in the door. According to Searle, the man should be able to use his book to translate them and then send back his own response in Chinese. Although he doesn’t speak a word of the language, Searle argues that through this process the man in the room could convince anyone on the outside that he was a fluent speaker of Chinese.

What it Means:

Searle conceived the Chinese Room thought experiment in order to refute the argument that computers and other artificial intelligences could actually think and understand. The man in the room does not speak Chinese; he can’t think in the language. But because he has certain tools at his disposal, he would be able convince even a native speaker that he was fluent in it. According to Searle, computers do the same thing. They don’t ever truly understand the information they’re given, but they can run a program, access information, and give a clear impression of human intelligence.

2. Schrodinger’s Cat

Schrödinger’s Cat is a paradox relating to quantum mechanics that was first proposed by the physicist Erwin Schrödinger. It concerns a cat that is sealed inside a box for one hour along with a radioactive element and a vial of deadly poison. There is a 50/50 chance that the radioactive element will decay over the course of the hour. If it does, then a hammer connected to a Geiger counter will trigger, break the vial, release the poison, and kill the cat. Since there is an equal chance that this will or will not happen, Schrödinger argued that before the box is opened the cat is simultaneously both alive and dead.

What it Means:

In short, the point of the experiment is that because there is no one around to witness what had occurred, the cat existed in all of its possible states (in this case either alive or dead) simultaneously. This notion is similar to the old “if a tree falls in the woods and there’s no one there to hear it, does it make a sound?” riddle. Schrödinger originally conceived of his theoretical cat in response to an article that discussed the nature of quantum superpositions, a theory that defines all the possible states in which an object can exist. Schrödinger’s Cat also helped to illustrate just how weird the rules of quantum mechanics really were. The thought experiment is notorious for its complexity, which has encouraged a wide variety of interpretations. One of the most bizarre is the “many worlds” hypothesis, which states that the cat is both alive and dead, and that both cats exist in different universes that will never overlap with one another.

1. Brain in a Vat

There has been no more influential thought experiment than the so-called “brain in a vat” hypothesis, which has permeated everything from cognitive science and philosophy to popular culture. The experiment asks you to imagine a mad scientist has taken your brain from your body and placed it in a vat of some kind of life sustaining fluid. Electrodes have been connected to your brain, and these are connected to a computer that generates images and sensations. Since all your information about the world is filtered through the brain, this computer would have the ability to simulate your everyday experience. If this were indeed possible, how could you ever truly prove that the world around you was real, and not just a simulation generated by a computer?

What it Means:

If you’re thinking this all sounds a bit like The Matrix, you’re right. That film, along with several other sci-fi stories and movies, was heavily influenced by the brain in a vat thought experiment. At its heart, the exercise asks you to question the nature of experience, and to consider what it really means to be human. The idea for the experiment, which was popularized by Hilary Putnam, dates all the way back to the 17th century philosopher Rene Descartes. In his Meditations on the First Philosophy, Descartes questioned whether he could ever truly prove that all his sensations were really his own, and not just an illusion caused by an “evil daemon.” Descartes accounted for this problem with his classic maxim “cogito ergo sum” (“I think therefore I am”). Unfortunately, the brain in a vat experiment complicates this argument, too, since a brain connected to electrodes could still think. The brain in a vat experiment has been widely discussed among philosophers, and many objections have been raised over its premise, but there is still no good rebuttal to its central question: how do you ever truly know what is real?

The only thing you can be sure of is that we exist. Yes, life may be just an impression, a lucid dream. But in order for you to be deceited, you have to exist. So life will always be true, even if it is a lie.

but an infinitely small life, since time is infinitely divisible, is also infinitely large. As long as life exists as a duration, not just a single moment in time, than between its beginning and end there are an infinite number of moments

“since time is infinitely divisible,” Except, of course, that time is NOT infinitely divisible. It occurs in discrete units, just like all other fundamental phenomena of the universe. and the smallest possible measure is one Planck Time (Google it). One Planck Time is 0.000000000000000000000000000000000000000000054 seconds. Anything shorter than that is meaningless, in physics. So there are a finite number of moments between the “beginning” and the “end” of any event, including life. Your days are numbered, and so are your Planck Times.

You can’t hold that life is illusory then try to use scientific knowledge gained through that illusion. For all you know, Planck’s time unit is a complete fabrication. The only types of thought that hold weight in an illusory world are thoughts which do not depend upon that world for evidence (such as formal logic or abstract thought). Since Planck’s time unit is based upon the travel of light in a vacuum it is therefore dependent upon evidence in this possibly illusory world. Thus, it is inadmissible as evidence to disprove that time is infinitely divisible.

Number 8 (The Ticking Time Bomb) poses the moral question – Is it right to torture one person in order to get information to save many more?
BLOODY RIGHT IT IS!
I have heard the PC brigade bleat on about Guantanamo Bay and human rights abuses going on there. So what? If it provides any information that stops another atrocity then it is right.
"But some of these people may be innocent" some of you might say. My parents told me if i played with matches I might get burnt! Every one of these "innocent people" I have read about have been questionable to say the least. One of these poor, innocent chaps, released to Britain, had used a false name and passport to leave the country before being captured.
Whilst I am on my soapbox, and as a British person, why are these detainees always referred to as British citizens (where i live anyway), when in fact they have been born elsewhere (usually in the middle east somewhere).

Torture the one to save the many! TOO RIGHT! If the person being tortured was a direct threat to the wooly hatted, vegetarian, petrol hating, hippy who is ranting about human rights then the hippy wouldn't be a shouting so loudly.

Kleanthis01 you make the argument that our outlook is changed if our loved ones are the ones in question,but this argument works both ways. What if it was your family/friends/significant other who was trapped in said city?

Haha you sound like the byproduct of a brainwashed fascist authority paradigm… Meaning, you’re completely controlled by fear and willing to dispense of inalienable human rights for safety. This is the greatest illusionary sham ever created. Every communist and totalitarian system stems from the disposition that it knows what’s in your best interest. So long as you let fear control you, your life’s efforts will remain futile.

#10 – Sure, you're responsible for the death of 1 person, but you are also responsible for saving the lives of five others. And I guess it depends on who the people are. If that person on the other track was your BFF, then you would not pull the lever.

Or, if the lever acts as a dimmer and not just an on-off switch, you can switch it to the halfway position which would cause the train to derail and kill nobody.

#9 – If the farmer openly stated that he knew the cow was in the field, then yes, he technically knew where his cow was – in the field. He just didn't know where in the field.

#8 – Call the bomb squad, evacuate everyone, and throw the terrorist right next to the bomb.

#6 – Evolution is the answer to all your problems.

#5 – I'm pretty sure this one has to do with covalent bonds between atoms. If there exist no covalent bonds between the rope atoms and feather atoms, or the rope atoms and hammer atoms; then the entire hammer+feather+rope cannot be regarded as one system, it must be regarded as three.

#2 – Keyword: quantum mechanics, not real-life stuff. In real life, you can only say "you just don't know", because a partially-dead cat would be like a zombie.

#1 – Kind of like "we don't know if the universe is going backwards in time [shrinking,] not expanding" because if the universe and everything within it was indeed going backwards, our minds would be thinking backwards. Two negatives cancel out, so we'd perceive time as going forwards.

You are totally missing the point of most of those you have commented on.

For #10, you are complicating an essentially simple moral question, and I really hope the bit about the lever acting as a dimmer was a joke.

For #8, I hope that too is meant to be a joke.

#6, what are you on about?

#5, utterly missing the point again, it’s not a matter of definition. Or, if you are actually suggesting that by fusing covalently they would suddenly fall faster, you don’t actually understand the theory of gravity…..

If some of those were actually a joke, sorry for missing it, but if not, then dear God read something on just one of these, because that was depressing to read.

You misunderstand Descartes' meaning. He posed that because you couldn't be sure that you are just a brain in a vat, this implicitly states that your mind must exist, because only that which exists can be deceived. "I think therefore I am" is therefore the ONLY statement you can make with 100% certainty. He was not "accounting for [a] problem"

In fact, he accounts for the demon problem by appealing to God’s existence and that He could never be a deceiver or allow us to be deceived in such a way. The person who wrote this shouldn’t just guess what Descartes said based on what he’s famous for saying, that’s sloppy stuff.

Also, wasn’t Gettier’s thought experiment called the “Sheep-Shaped Rock”? This could just be another philosopher’s version of the experiment however…

This is crazy. No one is crazy enough to hook up a brain to a computer. That is cruel and unusual. It is also impossible.

I will give you proof why I am right. If this supposed 'mad scientist' created an artificial world for you, then they would never let you find out about the 'brain in a vat'. They wouldn't want you to figure out what's going on.

Also, think about what you love in life. I'm not talking about material things. I'm talking about the stars in the sky, or when flowers are blooming in spring. You can't imagine them being artificial.

Think about yourself. You KNOW you are real. I am real. We are all real.

Most importantly, God created the world for us, not a mad scientist. Read the book of Genesis in the Bible to find out how the world was created.

Please don't let yourself be brainwashed by this 'brain in a vat' nonsense. You are too smart for that.

Don't let yourself be brainwashed by the Bible. Most of the stuff in the Bible is ten times more far-fetched than this stuff. And if you are going to take the book of Genesis seriously, then you have to take it ALL seriously, which is just ridiculous considering the Bible contradicts itself every other page.

Well, all sensory experience takes place in the brain. I'm afraid that you just don't know that you aren't a brain in a vat and that your Bible is just a byproduct of the evil scientists attempts to coerce into believing your reality is real.

I KNOW I am real. I DO NOT know that you are real, nor do you KNOW that I am real. However, because the claim that I exist is not so extraordinary, it takes very little faith to take this statement as truth.

You need to re-read the Cartesian method of doubt if you don't believe it makes logical sense, because I ASSURE you it does. Descartes was an extremely intelligent man and if you haven't read any of his work, it's pretty disrespectful to discard it as "nonsense."

I actually took my time to read the bible before I discarded it as nonsense.

Your "proof" also doesn't make any sense. If you are a brain in a vat…why would the scientist care whether you knew of the possibility of you being a brain in a vat? To you, this simulated reality is 100% convincing and as "real" as the "real" universe.

"I will give you proof why I am right. If this supposed ‘mad scientist’ created an artificial world for you, then they would never let you find out about the ‘brain in a vat’. They wouldn’t want you to figure out what’s going on."

I'm still waiting for your proof. How about you read Carl Sagan to find out how the world was created. I mean, you put your faith in a document written by man as it is. Why not put your faith in a document written by a smart one? As 'aquiredthoughts' says, the bible contradicts itself every other page. It's obviously a load of rubbish.

"Also, think about what you love in life. I’m not talking about material things. I’m talking about the stars in the sky, or when flowers are blooming in spring. You can’t imagine them being artificial."

First off, our brains process all those things, including our emotional reactions to them.

"Most importantly, God created the world for us, not a mad scientist. Read the book of Genesis in the Bible to find out how the world was created."

Second, what you're arguing is that no "mad scientist is controlling us," but that God created everything that we see, hear, touch, experience, etc… Therefore, I could argue that God is the mad scientist. Essentially, God and this "mad scientist" are creating human beings in a certain way, giving them free will and the capacity to gain knowledge. The only difference is believing in God is much more socially accepted, and a person gets a reward at the end of their lifespan if they are a good person. The scientist, however, is given a negative and "cruel" connotation.

If you believe that this theory is "impossible," then what makes God so much more likely? Granted, I am not saying I believe in either option necessarily; however, I do believe that blind faith is not nearly as reliable as science or facts.

"Also, think about what you love in life. Iâ??m not talking about material things. Iâ??m talking about the stars in the sky, or when flowers are blooming in spring. You canâ??t imagine them being artificial."

First off, our brains process all those things, including our emotional reactions to them.

"Most importantly, God created the world for us, not a mad scientist. Read the book of Genesis in the Bible to find out how the world was created."

Second, what you're arguing is that no "mad scientist is controlling us," but that God created everything that we see, hear, touch, experience, etc… Therefore, I could argue that God is the mad scientist. Essentially, God and this "mad scientist" are creating human beings in a certain way, giving them free will and the capacity to gain knowledge. The only difference is believing in God is much more socially accepted, and a person gets a reward at the end of their lifespan if they are a good person. The scientist, however, is given a negative and "cruel" connotation.

If you believe that this theory is "impossible," then what makes God so much more likely? Granted, I am not saying I believe in either option necessarily; however, I do believe that blind faith is not nearly as reliable as science or facts.

That’s one of the most illogical comments I’ve ever had the displeasure of reading.

Firstly, you make the assumption that ‘no one is crazy enough to hook up a brain to a computer’. Says who, exactly?

Secondly, you state that ‘they would never let you find out about the ‘brain in a vat”. Once again, how on earth do you know? That’s just a wild guess!

Thirdly, your thoughts are real, for they are being thought. But the stars? Saying you ‘know they are real’ has no rational reasoning behind it. Have you ever been sat down, and thought someone was standing behind you when they weren’t? Or carried on talking to a friend who had stopped a few yards back to do up their shoelaces? In these scenarios, you ‘know’ there is someone next to you – your senses deceive you. Why couldn’t the same occur in every single aspect of life?

As for ‘knowing’ that God exists, I am yet to hear a reason for doing so that does not, somewhere along the line, include a logical fallacy. Please, give me one?

Oh and finally, ‘don’t let yourself be brainwashed….you are too smart for that’. Are you actually a complete moron? It’s a thought experiment. It is actually suggesting that this is the case, only showing you that you don’t actually know if it is or not! Are you, by chance,desperately worried for the infinite number of innocent monkeys, forced into an eternity of typewriting?

No. 5: "In actuality, this story is probably just a legend; instead, it was this elegant thought experiment that helped prove a very important theory about gravity: no matter their mass, all objects fall at the same rate of speed." True, but only in a VACUUM!

that’s what i heard too! were they on the same page about the setting (vacuum or not)? i’m a bit too lazy to research about it right now…. aristotle is probably not talking about a vacuum if he’s considering drag.

what’s wrong with aristotle’s logic? wouldn’t galileo’s reasoning be a bit off if he tied a small parachute-like contraption to a small rock and threw it off a small building?

i didn’t really pay too much attention in my physics classes so a little enlightenment would be appreciated. =)

Mass has no effect on drag. Air resistance is caused by two things, the number of particles hitting the object, and their velocity relative to the object. This has nothing to do with the objects mass, and so it doesn’t matter whether Aristotle was imagining drag or not, it still has nothing to do with mass.

To give an example, if you drop two bricks, but one is denser than than the other, they will still fall at the same rate. They have the same drag, because they are the same shape and size, but their mass is different.

This is a very basic question about life, but it may also strike someone as nonsensical. What would it mean for someone else to be me? Or, what would it mean for me to be someone else?

These questions, which are not easily addressed empirically, can be dealt with by way of thought experiments.

First, I can imagine someone else being me if a duplicate were to be made of my body, with all my features, memories, habits, etc., and then if I were to be replaced by it. This was essentially the plot of the science fiction movie The Invasion of the Body Snatchers (1956, 1978), although the duplicates in those cases were not precise copies of the replaced individuals — they were actually alien beings that were duplicates to all external appearances, but not internally. However, it is not hard to imagine true duplicates being made, especially with the kind of technology imagined for the transporter machines in the Star Trek television series. The 6th Day, a recent Arnold Schwarzenegger movie (2000), was about just such complete duplicates. Nature itself produces duplicates, but only in the very first stages of life: Identical twins are genetically the same, but their experiences and memories begin to diverge as soon as the individuals start to develop separately — something already happening in the womb. A true duplicate of an adult would require a mapping of every atom in the body, which can now more or less be done with Nuclear Magnetic Resonance Imaging (NMR or MRI) technology, and then a duplicate set of such atoms being assembled in precisely the same way, something rather further from present technology. This would not be a “clone,” as presently understood, since a clone is only genetically identical. A clone would not have the same memories as the original individual, and it would be no more and no less like the original than an identical twin would be.

Could I be replaced with such a complete duplicate — every atom, not just genetically identical — it would think that it was me. But clearly it would not be me, especially if I were not destroyed in the replacement and continued to exist off somewhere else. We can imagine that such complete identity might produce a being that would simply see itself as existing in two places at once, but this would require some kind of communication; and that would require the existence of some kind of extrasensory or paranormal connection between the two bodies, which is not now part of established science. Without such paranormal communication, the identical individuals would each think of themselves as the original individual, although only one of them would be right; and they would immediately begin to diverge as individuals because of differing experiences.

So what would be the difference between the two individuals? Well, they would exist in different spatial locations, and they would consist of different, albeit identical, atoms — and it is a postulate of quantum mechanics that all particles of the same kind are absolutely identical. I know what it would mean for me not to be that other individual, since it would not be part of my consciousness. However, what if I were to be instantaneously destroyed and replaced with that individual, so that there was, to all appearances, a spatial continuity between us, and a material continuity since, as noted, identical material particles really are identical (there is, according to quantum mechanics, absolutely nothing about them that would enable us to tell them apart). If that individual would still not be me, then there would have to be something else about me that makes me myself apart from physical content, memories, and spatial continuity. In other words, I can perform the thought experiment that would remove “me” from my body, leaving behind an individual that looked, thought, and felt like me, but was not. It would simply not have my consciousness, but another one, which could then ask over again why it is itself and not someone else.

This same kind of thought experiment can be run the other way around: What would it mean for me to be someone else? I can easily imagine suddenly waking up and having another body. Franz Kafka wrote a famous story (“The Metamorphosis,” 1915) in which someone wakes up and has turned into a cockroach. I can also imagine suddenly losing my memory and not remembering who I am. This actually happens to people occasionally. It is also possible to imagine, as in the science fiction movie Total Recall (1990), that the memories of a different person have been put into me, and I wake up, not just not remembering who I am, but actually thinking that I am someone else. Combining these would produce a very dramatic effect: I might wake up both with a very different body and thinking and believing that I am a very different person. If this left me with at least the same brain, however, we would have no difficulty imagining how this could still be “me” in some accountable sense — it would still be my brain regardless of how the body around it might change or what kind of memories might be scrambled or reprogrammed in it. Interestingly, however, our own brain is usually something that we never experience; so were body and memories to be changed, it would be difficult to verify our personal continuity short of neurosurgery. From an internal point of view, and an external one for most practical purposes, everything would be different.

Now if I imagine body, memories, and brain to be replaced, then it would be easy to say that the result could not possibly then be me. However, it is still possible to imagine that the resulting individual could be me, and this act of imagination has actually occurred in multiple world religions for centuries: it would still be me if it were the same immaterial soul. Thus, if I were to believe in reincarnation, I would actually think that I have been innumerable different persons in the past, all with different bodies, memories, and brains. As Krishna says to Arjuna in the Bhagavad Gita: “I have been born many times, Arjuna, and many times has thou been born. But I remember my past lives, and thou has forgotten thine” [4:5, Juan Mascaró translation, Penguin Classics]. Krishna, implies, of course that memories of past lives are retained by the soul. This is not necessary to the thought experiment. It is possible to imagine a soul that does not carry memories but still carries an identical consciousness that would distinguish Arjuna from another individual physically and mentally identical. Since Arjuna (and most of us) does not seem to remember any past lives, this is what is given in experience anyway.

What the thought experiments demonstrate is a truth of metaphysics that the same attributes can belong to different individuals, or in other terms that an individual as an individual cannot be exhaustively defined by abstract predicates. Thus, bodily features, memories, personality, etc. cannot uniquely determine an individual; so I cannot identify myself as an individual by any such qualities. This metaphysical principle has only been disputed by philosophers like Leibniz, who postulate the identity of indiscernibles, that individuals that cannot be told apart are actually the same individual. But such a postulate only works for Leibniz because he denies the existence of space, which can serve to distinguish otherwise identical individuals.

The spatial separation of otherwise identical individuals also can be interpreted to mean that the individuals consist of different quantities of matter. To philosophers as diverse as Aristotle, Descartes, Spinoza, and Schopenhauer, different space and different matter are ontologically identical conditions: Space itself, in effect, is matter. This may now be restated in terms of quantum mechanics: If identical subatomic particles are postulated as absolutely identical by quantum mechanics, then spatial separation, again, is the only thing that individuates identical particles as materially different.

In the thought experiments on my personal identity, spatial or material difference might seem to do the job. An identical copy of me would be spatially and materially different, and if I were replaced by an identical copy, however quickly, it is still possible to imagine that it is materially different, even if instantaneously placed in the same space. However, such a transference would result in no externally ascertainable difference whatsoever, which sounds somewhat paradoxical if were are to say that the “matter” is different. In these terms “matter” must actually be defined in such a way that it is not materially or empirically distinguishable from other matter. Another postulate of quantum mechanics is that if two things cannot be in principle distinguished, then they are the same thing. The only thing that can distinguish identical particles is their spatial location. Thus, if we say that two individuals consist of identical particles and cannot be spatially distinguished (because they are temporally contiguous in the same space), quantum mechanics would then judge that they are the same individual. That there would be a temporal difference doesn’t help, since there is no empirical criterion by which it could be determined whether the “matter” has been switched from one moment in time to another or not. The only way in which we could then say that an identical individual could replace me instantaneously in the same space and still not be me is to require that there be a form of “matter” that is not accessible to physical science. A form of “matter” not accessible to physical science, however, would not be “matter” in any familiar or common sense meaning. An immaterial substance standing in the place of what we would ordinarily call “matter,” however, would more easily be called the “soul.”

If quantum mechanics loses track of matter by only using space to individuate identical particles, the thought experiment of me becoming a different individual contrariwise loses track of space and is only able to use matter for individuation. Thus, I can imagine instantaneously acquiring a different body, different memories, and also finding myself in a different place. If that is nevertheless still me, with my consciousness, it would have to be because the “matter,” or the substantial substrate of my self, was moved to that new location, even if nothing else moved by way of the contents and characteristics of my physical and mental identity. Since such “matter” would then be inaccessible to physical science, it would be reasonable to call such a substantial substrate “immaterial”; and an immaterial substance would reasonably be the “soul.”

It may help to recall what it would mean to say that I could find myself with a different body, a different mind, and in a different location and still be me. It would mean that the conscious existence that I experience now, the conscious existence that seems to disappear in sleep, and which I imagine, or suspect, or fear may simply become nothing in death, can still be imagined as the same conscious existence even if what appears in it is a different body, a different mind, and different place. Thus, I have not become nothing and can still be me, even if I seem to be someone else, cannot remember my old self, and have appeared in a different place. This conception of conscious existence as perfectly divorced from, and so possibly perfectly empty of, content first occurs in the Upanishads, especially the great Brhadâranyaka and Mândûkya Upanishads. Advaita Vedânta then concludes it is only the Self (Âtman) that has substantial, independent existence, while physical objects only exist as illusory appearances in consciousness.

Although “matter” in the senses examined, whether physical or immaterial, is a metaphysical conception that is not accessible to physical science, the device of thought experiments to examine these issues is a perfectly legitimate procedure, not only for philosophy, but even for physical science itself: Einstein’s entire theory of Relativity was based on his own thought experiments. Thus, the basic question here, “Why am I myself, rather than someone else?” is no more dismissible than Einstein’s question about what a light wave would look like if we were moving at the velocity of light with it. The paradox, however, of ending up with a definition of “matter” that abstracts from it all identifiable qualities was not lost on Buddhism, which rejected the idea of a substantial substrate to anything. Like Hume, Buddhism adopted a kind of empiricism where the very conception of substance, whether material or immaterial, did not qualify. However, that produced its own paradoxes, since Buddhism, like Hume, could not then account for the duration in time of objects or persons. Much of Buddhism accepted the doctrine of “momentariness,” that individual objects do not abide for more than a moment, but this is considerably more paradoxical and counter-intuitive that the duration of a substantial substrate. What the Buddhist paradoxes show us is that the substrate, however intangible, is not an unnecessary hypothesis — without it, as a synthetic ground a priori (as Kant would put it), the duration of individuals cannot be accounted for.

Instead, I must appeal to the doctrine of The Origin of Value in a Transcendent Function. Both kinds of “matter” are conceptions of “Negative Transcendence,” the emptiness of existence over and above the phenomenal content of consciousness. Negative Transcendence has internal and external poles. External transcendence then corresponds to physical substance, which in terms of quantum mechanics, as we have seen, is functionally identical to space itself. Internal transcendence is then the substrate for the sense of personal identity that has been examined here in the “thought experiments on the soul.” The question left open in The Origin of Value in a Transcendent Function was in what way internal and external transcendence corresponded to each other.

Now it appears that internal and external transcendence must in an important sense be independent of each other, since external transcendence, as space, cannot account for personal identity from an internal point of view, and internal transcendence, as the “matter” of personal identity, varies independently of space and what can be accessed by physical science. Thus, for there to be personal identity, there must be more than just space and external transcendence. Such a conclusion, however, does not produce a Cartesian Dualism of material and immaterial substances existing in the same logical space, for internal and external transcendence are kept ontologically apart. They are only united through “Positive Transcendence.” Negative Transcendence, in other words, cannot be added as a transcendent object to the order of phenomenal objects. Transcendent objects are subject to the Kantian Antinomies. Rather than being added as a transcendent object to phenomenal reality, internal transcendence casts a “shadow” of Positive Transcendence on phenomenal objects: the numinosity of the self or soul in religious conceptions, or even just the “supernatural dread” associated with dead bodies or cemeteries.

The question, “Why am I myself, rather than someone else?” then, cannot be answered just with natural objects. It can only be answered with transcendence. But transcendence appears in the phenomenal world as the numinous quality of natural objects. This may be called the “soul.” The soul, as an independent, transcendent object, however, cannot be said to be established by this argument. The fact that Buddhism rejects such an object is an important clue that it is subject to the undecidability of a Kantian Antinomy. There is no doubt, on the other hand, of the numinosity of persons in Buddhism, especially as they become Bodhisattvas and Buddhas, and of the reality of karma and reincarnation, despite the denial that reincarnation is the transmigration of a substantial self. Buddhist doctrine thus expresses the paradox of Negative Transcendence as an existence which nevertheless cannot be placed as an object in conceivable (i.e. phenomenal) reality. Later this would be conceived as the “Buddha nature” of individuals, an idea that, not surprisingly, set off controversy about whether this involved a “substantialist heresy” or not. It is, indeed, a fine line, although easily drawn with the theories of Negative and Positive Transcendence.

Postscript

As noted, it is a postulate of quantum mechanics that subatomic particles in the same quantum states are absolutely identical in characteristics. Although many have believed that Einstein vindicated Leibniz’s view of space, as relative, over Newton’s, this feature of quantum mechanics decisively contradicts Leibniz, for whom space does not exist and objects that are indistinguishable from each other are identical to the same thing. But indistinguishable electrons are not identical to the same thing. They are distinguished from each other by their locations in space (although their possible locations may be summed in the wave function). Leibniz, of course, could respond that what makes the electrons different is their history, and their relationship to other objects. However, while Leibniz believed that his “monads” contained their history, and a representation of their relationships, within themselves, this is not the case for electrons. Indeed, quantum mechanics rules out any such things as “hidden variables.” With an electron, what you see is what you get. And since Leibniz’s monads don’t actually interact with each other, the only terms of their history and their relationship with other objects are their motions and relationships in space. If space does not then exist, monads actually have no history and no relationships.

If we allow that identical objects, however, are distinguished by their locations in space, location in space will not work to account for identity. That is because, as an object moves, it comes to be at a different location. So if different locations serve to distinguish different objects, why does not a object become a different object by moving and coming to be in a different location? This poses a grave difficulty for the theories of matter in Descartes and Spinoza, where matter is all but indistinguishable from space itself. But space does not move around, while matter must move around, to maintain its identity. On the other hand, it is not clear that fundamental particles in quantum mechanics possess any “matter” in the traditional, substantial sense. Energy turns into electrons and positrons. Electrons and positrons collide and turn back into energy. What we see is a collections of attributes, or quantum numbers — mass, charge, spin, etc. — that looks like nothing so much as the “aggregates” (skandhas) of non-substantial existence in Buddhism.

Unfortunately, the denial of substance in Buddhism is intended to effect a denial of identity. If the problem is accounting for the identity of an object or sub-atomic particle from moment to moment, Buddhist metaphysics is specifically designed not to do this. The result is an effective thought experiment in what is required for identity: The “aggregates” are not enough. If an electron has an enduring existence, something has the mass, charge, spin, etc. that characterize it. And if the electron, as electron, ceases to exist, neither Parmenides nor Democritus would be surprised to learn that it does not simply become nothing. Mass/energy is conserved, and there are particles that carry them away. Matter will not be a Cartesian fixed quantity of “stuff” that no transformation can alter, but it will represent a durable continuity of identity, which carries the quantum attributes and can merge with other objects or itself divide into new objects.

This, indeed, is more an Aristotelian than a Cartesian view of matter. Perhaps the only difference is that Aristotelian matter only accounts for different individuals of the same kind. Something unique of its kind (sui generis) doesn’t need matter and can exist as pure form (like God or the celestial intelligences). In the argument here, however, material substance does not merely account for different things of the same kind, or for different individuals that are otherwise identical in every way, but also for the identity of anything with itself from moment to moment — and Aristotle’s substance (ousia), after all, was in the form, not the matter. A Buddhist analysis of Aristotle’s God would be that it has no self, no identity, and duration. Probably not what Aristotle wanted to say, but then he is vulnerable to the critique, since for “substance” he can only offer attributes, i.e. the form.

While Aristotle thought of form as substance, it might be noted that a curious thing happened to the terminology in the translation from Greek to Latin. Ousia is from the participle of the verb “to be” in Greek. Thus, it looks rather like essentia, “essence,” in Latin, which is from the infinitive of the verb “to be” (esse). Substantia, “substance,” itself, is entirely different, meaning to “stand under.” There is a word that means “stand under” in Greek, and that is hypokeimenon. Aristotle does not use that synonymously with ousia. He applies it, as it happens, to matter. Perhaps it would be better to translate ousia as “essence,” in which case we could take substance, the underlying thing, as always being what Aristotle associated with matter. His reluctance, however, is understandable, since he thought of matter as mere power or potential, which would disappear in God. By the time we get to St. Thomas, of course, that idea of a powerless God was unappealing.

If our concern then becomes personal identity, will the identity of material substance account for that? As I have argued, no. In physical terms alone, we know that there is a turnover of matter in our bodies. I believe that after 20 years or so, all the matter in our bodies is supposed to be different. A defendant in a legal case once even tried to argue that he was literally not the same person who had committed the crime, some twenty years plus in the past. His argument was not allowed as, indeed, we trace personal identity across that transformation. With the material objects, this can indeed produce some paradoxical results. The Stoics noticed that in their day the ship kept at Athens, which was supposed to have born Theseus to Crete, had finally been repaired so much that every single plank and other part of it was no longer original. Was it the “same” ship? In a way yes, and in a way no. With material objects, the less the original material, the less it is the original thing. There is no such ambiguity with people. And we can ask them.

Similarly, we can use the thought experiments detailed above. We can think of ourselves persisting even through transformations in body, memories, and everything else. We can even, as it happens, think of ourselves persisting through absences of consciousness. Indeed, we do that every day, as we awake from sleep. This would be challenging for Descartes, for whom the soul was essentially thinking, or for Advaita Vedanta, where the self (âtman) is essentially conscious. But it is not really a problem — consciousness is not essential to identity when the identity of consciousness from moment to moment must itself be accounted for. If personal identity requires a substantial substrate different from material existence, our word for it would be “soul.” This would be a different and more fundamental meaning for it than what soul was for the Greeks, the life force, or for Descartes, consciousness (Searle’s “mental substances”).

The remaining problem would be the epistemological one of why we believe there are substances at all. Not only Buddhism, but Berkeley and then, especially, Hume point out that since substances are behind or beneath everything we experience, we are not directly acquainted with them as such. So what is our evidence that there are such things? The Kantian argument of the “possibility of experience” is then that “substance” is a category, like causality, which is an a priori expectation about experience, not something deduced, derived, or proven from it. Our expectation that the existence of objects is durable, separable, and identical is the principle of “substance” by which we organize and understand experience. While Hume himself said that all reasonings about matters of fact are based on the relation of cause and effect, it is obvious enough that many such reasonings are also based on the persistence, independence, and identity of substance.

What Kant would ask, of course, is what we can know about a substantial soul outside the limits of a possible experience. The soul, after all, is not a natural or phenomenal object, and it is difficult or impossible to imagine how it can exist, as a substance, in the phenomenal world. Kant’s answer then is that the limits of possible experience represent the limits of our knowledge of objects, so that we do not know how it is that substantial souls can exist. An immortal soul, which would be immune to the slings and arrows of man and nature, is in that regard an unconditioned reality, the sort of thing that does not appear in phenomenal existence, either for Kant or Buddhism. Yet even Buddhism does not deny that there are unconditioned realities — most importantly Nirvana. Thus Buddhism, which is ultimately neither materialistic nor naturalistic, actually has more in common with Kant than it does with Hume or, for that matter, John Searle. The soul as a numinous reality, is fully present in the numinosity of the Buddhist Arhat, Bodhisattva, and Buddha. This is no comfort for the materialist, the skeptic, or the nihilist.

The answer given for #4 is, of course, not correct: The monkeys never can type the entire works of Shakespeare, nor any other similar volume of text, in any realistic amount of time. The reason is simple: each time a monkey starts getting a string of text right, it is far more probable that he will get next keystroke wrong than right, thus invalidating the entire string. The longer the string gets, the more improbable it becomes that the next letter will be correct. For short sequences (just a few letters) the monkey might get it right by shear chance, but for anything longer than a half dozen words, it just won’t happen. Not even in the entire age of the universe.

Think of it this way: Assume that the monkey has a keyboard that can produce 26 uppercase letters, 26 lowercase letters, and a half a dozen punctuation marks (space, full stop, comma, quotes, exclamation mark, and question mark.) That makes 60 characters. The monkey starts typing at random, and produces a “W”, which happens to be the first letter of the first line in Macbeth: (“When shall we three meet again”). Let’s say “the force is with him”, and on the next few keystrokes he hits an “h” an “e” an “n” and a space. Great! Now he has entire first word right! The problem is, on every single “next keystroke”, there are 59 ways the monkey can be wrong, and only one way he can be right. If he does not hit an “s” then everything he has typed so far is useless, the entire text must be scrapped, and he has to start again.

Ooops!

He is 59 times more likely to hit the WRONG key than the RIGHT one, at random. He only has a 1 in 60 chance that the next letter will be correct.

But this isn’t just a matter of adding up the letters and multiplying by 60: this is an exponential problem. The chances that he will get two letters in a row correct are one in 60×60, which is also written 60^2, which works out to 3600. So he’d need to type 3600 random keystrokes to be stand a good chance of producing the first two letters (“Wh”)

The chances of getting three letters right are 1 in 60^3 (60x60x60), which is one in 216,000. For 4 letters is one in 12,960,000. To get “When” right, he’d need to type about 13 million keystrokes! Maybe you are starting to get the picture…

Mathematically, the chances that he’ll get “n” letters correct are 60^n (“60 to the power n”, which is the mathematical way of saying “there are 60 ways of getting each of “n” letters.).

The entire first line of Macbeth (“When shall we three meet again?”) has 31 characters, so the chances of the monkey getting it right are 60^31, which is roughly one in 1,326,443,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Wow!

Let’s say this monkey types really fast, never sleeps, eats or takes vacations, and can tap out 10 characters per second. So roughly every 3 seconds he will produce a line of text that we can compare against that first line from Macbeth. How long will it take the monkey to produce that line? One sample every 3 seconds is 20 samples per minute, which is 1200 per hour, 28,800 per day, and 10,519,200 per year. Ten million samples per year! Not bad…. At that rate, it will only take the monkey a bit more than a year to type the single word “When” correctly, and about 126,097,376,067,039,332,591,704,312,114,990,000,000,000,000,000 years to get the entire first line of Macbeth correct! Well, it turns out that, so far, the entire universe has only aged about 15,000,000,000 years (give or take a billion), so that poor hard-working monkey is going to need a bit more time…

So we add more monkeys! Let’s be generous and put not just ONE monkey to work, but a BILLION monkeys to work. Cool! Between them, it will only take them about
1,260,973,760,670,393,325,917,043,121,149,900,000,000 years! That’s MUCH better, isn’t it?

Hmm, so it seems a billion monkeys working for the entire age of the universe isn’t enough. So let’s get REAL generous, and say that there will be one billion monkeys on each of one billion planets in each of one billion galaxies… how does that work out?

Turns out, we are now down to just 1,260,973,760,670,393,325,917 years! Or roughly 840,649,173,780 TIMES the age of the universe.

In other words, a billion billion billion monkeys, typing for the entire age of the universe, (ever since the Big Bang and right up to now), multiplied eight hundred and forty billion times over, stand a roughly even chance of producing ONLY THE FIRST LINE OF MACBETH correctly!!!! Just 31 characters.

Maybe now you get to see why this is such an incredibly improbable feat! And that’s just for a very simple phrase: “When shall we three meet again?”.

But Shakespeare wrote quite a bit more than just 31 characters. There are roughly 130,000 characters in “Macbeth”, so instead of the problem being just 60^31 it is actually 60^130,000 for just that one play (Macbeth). But Shakespeare wrote a total of 38 plays, 154 sonnets, two rather long poems, and several shorter poems. ….

Sorry, but that ain’t gonna happen. Not even if you could miniaturize the monkeys, and speed them up a thousand times. In fact, not even if you could get every single atom in the entire known universe typing out text at the rate of millions of characters per second! Even then, you STILL could not get the job done in any realistic amount of time. Not even in an incredibly unrealistic amount of time!

(And all of this is without even considering who is going to CHECK what the monkeys typed, compare it against the works of Shakespeare, and see if they got it right or not…)

That’s the difference between theory and reality. Yeah, with an “infinite” amount of time and an “infinite” number of monkeys you could do it, in theory, but NOT with any realistic scenario of time, monkeys, typewriters or text.

So the claim the correct answer is that all those monkeys and all those typewriters don’t stand even the vaguest chance of producing even the tiniest fraction of the works of Shakespeare. #4 is wrong.

the beauty of the concept of “infinity” is that compared to infinity 1,326,443,500,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 raised to itself is almost just like a speck of dust in this… errr…. dusty universe…. in short, unimaginable. who knows, with all those monkeys one may have been bitten by a radioactive clone of shakespeare that has given that said monkey the super power to not only remember all his works verbatim but also type it using a typewriter (heck, if i can think it then it’s probably one of the infinite possibilities, right?)……… “Realistic” has been thrown out of the window when the term “infinite” was used. u don’t need crazy mathematical skills to get the point of this thought experiment, u just need your imagination! =D

For waaaaaaaaaayyy too many of these comments, people are not grasping a) the point of a thought experiment in the first place (it’s not literal) and b) the idea or concept behind the experiment! Infinity is a concept, a never ending number. The authors for instance never claimed that we should actually rely on monkeys to type Shakespeare. In the scenario of an infinite number of monkeys with an infinite number of typewriters, every keystroke that goes on has an infinite number of chances at being the correct keystroke, so some of the monkeys get it right one letter at a time. The odds of the next keystroke being correct as well are incredibly slim, but that is where the element of infinite time factors in. Given enough time, these monkeys WILL type every possible combination of characters imaginable, and within those possible combinations will be every written work known to man. The thought experiment never claimed that this would happen in “a reasonable amount of time.” Maybe the give away was the “infinite amount of time” factor. Regardless, please don’t waste your time attempting to poke meaningless holes in a THEOREM by which you are simply spreading your own ignorance of a concept rather than learning for yourself.

When people have to resort to insults and straw-man arguments in their vain attempt to defend an indefensible position, all that it shows is that they don’t actually have any basis for their superfluous wafflings and splutterings at all!

The point, of course, is that infinite time changes nothing: with every single keystroke, it becomes statistically more and more UNLIKELY that the monkeys can ever type the entire works of Shakespeare! I did, of course, point this out in the very first paragraph of my original post:

“The reason is simple: each time a monkey starts getting a string of text right, it is far more probable that he will get next keystroke wrong than right, thus invalidating the entire string. The longer the string gets, the more improbable it becomes that the next letter will be correct.”

Got that last part? “The longer the string gets, the more improbable it becomes that the next letter will be correct.” In other words, as time goes on toward infinity, then chance of getting it WRONG increase, not the chances of getting it RIGHT.

In other words (for those who seem to have a problem understanding basic high-school statistics, and simple logic), each time that a monkey types a letter, the chances that he will get the next letter WRONG increase EXPONENTIALLY, while the chances he will get it RIGHT only increase LINEARLY. It doesn’t take very long before the probability of getting it wrong approached infinity… And each time a monkey strikes yet another key, the probability that he will fail at the task get even closer to 1, while his chances at succeeding get closer to zero.

On the very first keystroke his chances his chances of getting that one right are very high, but on the second keystroke, the changes drop dramatically. By the twentieth keystroke, his chances are so close to zero as to be not worth mentioning, and as time progresses, his chances get every closer to zero, and not only that, they ACCELERATE towards zero.

The belief to the contrary is, of course, closely related to the gambler’s fallacy: The gambler believes that a string of unbroken losses means that his chances of winning on the next bet are improving, when in fact they are not. The inverses case for the monkeys is similar (although infinitely more negative) : A string of unbroken “wins” (hitting the correct letter) does not increase the chances of success, and in fact increases the chances of FAILURE.

And no, the fact of extending the experiment for an infinite amount of time does NOT make it more probable that the monkeys will eventually succeed: In reality, it makes it infinitely more likely that they will continue to fail, eternally. Inability to see this rather obvious implication is a clear indication of your basic misunderstanding of statistics and the concept of infinity. Despite what intuition tells you, actual reality is somewhat different. No, that’s not a personal insult: it is simply a statement of fact.

So, if you can’t grasp the simple basics of statistical analysis, then maybe you shouldn’t post unfounded opinions on the internet: That way, you could avoid embarrassing yourself further.

The mere fact that you attempted to embarrass ME into not refuting your childish position is a glaringly obvious indicator of your fear of being refuted. Which, I believe, I have accomplished rather successfully anyway. (And which, of course, is your cue to spew forth yet another unfounded, infantile response of meaningless drivel.)

Don’t forget the infinite monkeys, infinite typewriters, and infinite time. I think you’re trapped into seeing a finite amount of monkeys. If that were the case, then the chances would be decreasing as such. But the probability of recreating such Shakespearean works given infinite monkeys, and infinite time…with the use of infinite keyboards surely must be 1. The probability of each monkey getting it is so small that it would approach zero, but the probability of one of them getting it eventually would approach 1.

Except that there is also an infinite number of possibilities that do not contain the works of Shakespeare. Thus making it possible that even with infinity and an infinite number of monkeys, they may never type the complete works of Shakespeare.

The probability of each keystroke is completely independant of everyother keystroke. The overall probability of the monkeys writing all of billy shakes’ works is inconcievably low before said monkey begins, but becomes exponentially greater each time he selects the correct key. For example, the probability of getting tails twice in a row when fliping a coin is .25, right? But if you flip the coin and get tails once, the probability rises to .50, because the first variable has become a certainty (1.0).
And beside that, assuming assumingall the mokeys are working at once, one failure wastes little time or energy, because there are infinite other monkeys typing away, at least a few of them are already killing off there third or fourth character by now.
Remember, nobody ever said the circumstances were possible, but given such generous circumstances it is almost certain that the works will come out in a few years.

“In other words (for those who seem to have a problem understanding basic high-school statistics, and simple logic), each time that a monkey types a letter, the chances that he will get the next letter WRONG increase EXPONENTIALLY, while the chances he will get it RIGHT only increase LINEARLY. It doesn’t take very long before the probability of getting it wrong approached infinity… And each time a monkey strikes yet another key, the probability that he will fail at the task get even closer to 1, while his chances at succeeding get closer to zero.”

Those two statistics don’t exist at the same time. They can easily even be considered the same statistic based purely on respect to temporal perspective. Each additional character required causes the initial probability of failure to approach infinity. Each additional character gotten correct, from that point on, literally decreases the amount of required characters for that instance, causing the probability of success to approach 100%. Each incorrect character merely resets the counter. The statistic you keep bringing up is more akin to a starting line and can’t change once monkeys are started typing.

What’s more damning, however, is that that “exponentially increasing” statistic is rooted in the single finite variable in the entire experiment: the length of The Complete Works of Shakespeare.

Because the length of The Complete Works of Shakespeare is finite, it will always be infinitely less than infinity. This is the crux that your argument neglects.

No matter how infinitesimally small the probability of a monkey producing The Complete Works of Shakespeare is, with infinite monkeys and infinite typewriters, you’re directly comparing a finite number to infinity.

You don’t even need infinite time. All possible occurrences are happening simultaneously with the monkeys alone and the time it takes to produce The Complete Works of Shakespeare is literally the shortest time possible for a monkey to type it. There will be an infinite amount of failures and an infinite amount of successes because everything that could ever happen will happen at once an infinite amount of times. All your calculations are ultimately meaningless because infinity breaks math. Once it’s introduced, there’s really only two numbers: infinity and not-infinity. This is why calculus is so convoluted; it bends over backwards to avoid this.

I think Chileman2020 has not in the least grasp of the word infinty.
When we are talking of infinte universe, anything having probability of more than zero will recur not 1, 2 but infinite times.so even if probality of monkeys typing the series is 1X10^-100000……
it will happen infinite times.There will also be infinite harry potter collections , infinite oxford dictionaries as well as infinite times aaaaa…./bbbbb…./cccc…. etc.

There are an infinite number of numbers on the decimal line between 1 and 2, but none of them are other whole numbers. Just because you have an infinite series does NOT mean you can count on everything being contained within that series. There are still probabilities in infinite series, especially since we cannot directly observe and quantify the things within that series. That is why it can be said that in an infinite series things may be more or less likely to occur. For example, in this mind experiment it is far more likely that infinite monkeys will poop, play, mate, and fight each other than they are to make intentional keystrokes. The point of the thought experiment is to say that a RANDOM element has the ability to produce non-random things (such as all of Shakespeare). The problem is, random elements cannot be quantified.

If you put a truly random element in a scenario (monkeys are actually pretty predictable) there is NO possible world (a way of saying that no matter how you couch the mind experiment it won’t work) where you can say for certain that the truly random element will produce anything. You cannot even say that the random element will produce nothing (since it is random). Every “set” is possible to the random element but NO set can be proven actual even in an infinite space, with infinite elements, infinite time, and infinite materials. And don’t try to argue that by proving that no set can be proven I’ve proved that the set “no set can be proven” is proved. That is a logical absurdity and to argue it is to cut your own legs off.

I really don’t get Schrodinger’s Cat….. can someone dumb it down further to the level of a 10 year old for me? haha… i’ve tried reading up on quantum mechanics, but somehow my brain refuses to absorb any of it. what exactly is Schrodinger arguing against and what’s his point when actually applied in quantum mechanics?

“because there is no one around to witness what had occurred, the cat existed in all of its possible states”. this particular line doesn’t make sense to me. it’s just dead OR alive so how can anyone say that the cat existed in all of its possible states just because no one knows what happened to it? is this based on an external observer’s viewpoint?

Well, I could explain it to you (it’s actually not hard to understand at all), but I seem to have used up all my “time to waste” (as you call it) on showing why Number 4 is not correct for any conceivable universe… Sorry!

( But here’s a hint: The Schrodinger’s cat paradox is based on observation, just as the entire universe is based on observation. And it has nothing at all to do with anyone observing the cat. The experiment, as laid out here, is not stated correctly as a demonstration of quantum mechanics: If it were, the cat actually would be both alive and dead at the same time, in exactly the same manner as particles on the quantum scale being in multiple indeterminate states at once, until observed. )

Because the state of the atom determines if the cat is alive or dead and because quantum physics proposes that the atom is in the state in which the cat is both alive and dead, it means that quantum physics do not translate into the real world. That’s why people are trying to find a Universal Theory (such as the proposed String Theory) because quantum mechanics and gravity (i.e. small math, large math) do not agree with each other, yet they are both correct in their calculations.

How can #2 be called a Paradox? Its often described as a paradox. But I don’t think its really thought of one at all by physicists. The apparent paradoxical part is the cat is both alive & dead, but what about single atoms & quantum states? They are in superposition & ill defined just like the cat. How can it even be described a paradox if the measurement problem is still unresolved? And than adding decoherence? The experiment only deals with the copenhagen interpretation & argues that it is absurd especially when scaled up to macro scale.

“The probability of each keystroke is completely independant of everyother keystroke. ”

and

“the probability of getting tails twice in a row when fliping a coin is .25, right? But if you flip the coin and get tails once, the probability rises to .50, because the first variable has become a certainty (1.0).”

Both statements cannot be true, and indeed are not true. The first is correct, the second is the “Gambler’s Fallacy”. Prior coin tosses have zero influence on future coin tosses, just like prior keystrokes have zero influence on future keystrokes.

Keystrokes and coins are no different from each other. Each act of flipping a coin is completely independent of every other act of flipping a coin. The odds do not change just because a particular outcome already happened, or did not happen.

That’s a great list; the brain in the vat experiment is particularly interesting but I’d love to try out a virtual reality. I’ve heard people saying that the The Matrix ripped off the idea but The Matrix is actually based on Simulacra and Simulacrum, a book that deals with hyperreality, written by Jean Baudrillard.